Currently I am shooting a thompson center .204 and it has no trouble at all in leveling a coyote, and it is just a fantastic caliber to shoot. I have also used my .300 wm and shotguns, my dad uses his 22-250. But it doesn't matter what you use it only matters if you are enjoying it and killing some yotes.

I have a gp100 in .357 that i love to kill dogs with. I always carry it along with either my ar or my bolt gun. The choice of the second rifle depends on the area I am hunting. In easter WA. I usually bring the bolt gun in western WA. I stick to the ar, these choices are more baised on the rifles set up than personal preferance. The fn pbr is set up fro long range with a millet 4-16x55 optic. The ar however is set up with a decent eye relief for fast targeting. I built the ar from the floor up and set the optic plaform in a forward scout position. Seams to work well in the tight confines of western washington forests.

Howa 1500 in 22-250 is my go to gun on yodel dogs, with any reliable shotgun that will eat hevi shot dead coyote loads as a back up. Man I do love that stuff and they can be way out there for a scatter gun with it

Not so many predators over here but I run almost all bolt guns and shotguns even though I have permitted semi autos.
Foxes its a Mod 70 .222, Rem 700 .22-250 or T3 25-06 we dont keep skins .
For Wild dogs on the rare occasion I get to hunt them its the 25-06 or CMC .300win mag.
And Feral Pigs a major predator here its any thing from the 22-250 to the 450 rigby and the pump shotguns.
I also shoot a lot of feral cats but for those I prefer a .22 cal 40gn travelling at better than 4000fps like the 22-250 or a 220swift.